Data Storage:

Mostly every kind of game needs it, storing data, for various purposes, storing options configuration, achievements, information about levels, scores and so on. Android library, 
by default it gives us opportunity to use two ways.

1. Shared Preferences.

Simple Interface for accessing and modifying preferences. Devoted rather for parts of data. Useless to explain how to use it - since its well explained here (official Android infos) There are no differences in usage, no matter when you want to use it, there is no need for special description for AndEngine developers.

2. SQLite Databases.

Store structured data in a private database. Especially useful for storing info about levels, scores, achievements and similar data. Its also well explain - here. 

If you need code example, how to create example database with table and few fields inside, you may follow code shared by RealMayo - HERE. He provide well commented code, so you shouldn't have any problems with understanding how does it work.